Generalized monotone mixed variational inequalities

Generalized Variational-like Inequalities with Compositely Monotone Multifunctions

In this paper, we introduce two classes of generalized variational-like inequalities with compositely monotone multifunctions in Banach spaces. Using the KKM-Fan lemma and the Nadler’s result, we prove the existence of solutions for generalized variational-like inequalities with compositely relaxed η − α monotone multifunctions in reflexive Banach spaces. On the other hand we also derive the so...

Generalized Projection Method for Non-lipschitz Multivalued Monotone Variational Inequalities

We generalize the projection method for solving strongly monotone multivalued variational inequalities when the cost operator is not necessarily Lipschitz. At each iteration at most one projection onto the constrained set is needed. When the convex constrained set is not polyhedral, we embed the proposed method in a polyhedral outer approximation procedure. This allows us to obtain the projecti...

A New Method for Solving Monotone Generalized Variational Inequalities

We suggest new dual algorithms and iterative methods for solving monotone generalized variational inequalities. Instead of working on the primal space, this method performs a dual step on the dual space by using the dual gap function. Under the suitable conditions, we prove the convergence of the proposed algorithms and estimate their complexity to reach an ε-solution. Some preliminary computat...

Generalized Variational Inequalities Involving Relaxed Monotone Mappings and Nonexpansive Mappings

Generalized Nonlinear Mixed Quasi-variational Inequalities Involving Maximal Η-monotone Mappings

In this paper, we introduce and study a new class of generalized nonlinear mixed quasi-variational inequalities involving maximal η-monotone mapping. Using the resolvent operator technique for maximal η-monotone mapping, we prove the existence of solution for this kind of generalized nonlinear multi-valued mixed quasi-variational inequalities without compactness and the convergence of iterative...